Rotational partition function

Rotational energies are quantized. For a diatomic molecule like CO or HCl, the allowed rotational energies are $E_{rot}=\frac{\bold{J}^2}{2I}=\frac{j(j%2B1)\hbar^2}{2I}=j(j%2B1)\epsilon$

The number of degenerate states g_j for each level j is 2j+1. The rotational partition function is therefore $Z_{rot}=\sum_{j=0}^{\infty}g_je^{-E_j/kT}=\sum_{j=0}^{\infty}(2j%2B1)e^{-j(j%2B1)\epsilon/kT}$

Statistical mechanics

Statistical ensembles	Microcanonical • Canonical • Grand canonical • Isothermal–isobaric • Isoenthalpic–isobaric • Open

Statistical thermodynamics	Characteristic state functions

Partition functions	Translational • Vibrational • Rotational

Equations of state	Dieterici • Van der Waals • Ideal gas law • Birch–Murnaghan

Entropy	Sackur–Tetrode equation • Tsallis entropy

Particle statistics	Maxwell–Boltzmann statistics • Fermi–Dirac statistics • Bose–Einstein statistics

Statistical field theory	Conformal field theory • Osterwalder–Schrader axioms

See also	Probability distribution • Structureless particles